Option pricing under a financial model with stochastic interest rate

In finance, stochastic volatility models at which the interest rate is also stochastic have the ability to fit better with the structure of the market. Although the models furnish more reliable outputs, they are challenging to be tackled with due to higher involved dimensions. The purpose of this work is to introduce and solve one of such models efficiently, which is known as the Heston CIR pricing equation formulated as a partial differential equation. The idea is to transfigure the continuous problem into a system of discretized equations. Results for one test is also reported.